We derive a delay-dependent H∞ performance criterion with a decoupled structure for systems with neutral time delay. We then extend it to an H∞ controller synthesis for systems with polytopic uncertainty. All conditions are given in terms of linear matrix inequalities (LMIs). In some previous descriptor system methods, the products of the controller and Lyapunov matrices are completely separated for the performance analysis, but not for controller synthesis - the method developed in the current paper eliminates this weakness. We present a numerical example to illustrate the effectiveness of the solution.

In this paper, we discuss the crucial but little-known fact that, as Kolmogorov himself claimed, the mathematical theory of probabilities cannot be applied to factual probabilistic situations. This is because it is nowhere specified how, for any given particular random phenomenon, we should construct, effectively and without circularity, the specific and stable distribution law that gives the individual numerical probabilities for the set of possible outcomes. Furthermore, we do not even know what significance we should attach to the simple assertion that such a distribution law “exists”. We call this problem Kolmogorov's aporia†.

We provide a solution to this aporia in this paper. To do this, we first propose a general interpretation of the concept of probability on the basis of an example, and then develop it into a non-circular and effective general algorithm of semantic integration for the factual probability law involved in a specific factual probabilistic situation. The development of the algorithm starts from the fact that the concept of probability, unlike a statistic, does not apply to naturally pre-existing situations but is a conceptual artefact that ensures, locally in space and time, a predictability that is more stable and definite than that permitted by primary statistical data.

The algorithm, which is constructed within a method of relativised conceptualisation, leads to a probability distribution expressed in rational numbers and involving a sort of quantification of the factual concept of probability. Furthermore, it also provides a definite meaning to the simple assertion that a factual probability law exists. We also show that the semantic integration algorithm is compatible with the weak law of large numbers.

The results we give provide a complete solution to Kolmogorov's aporia. They also define a concept of probability that is explicitly organised into a semantic, epistemological and syntactic whole. In a broader context, our results can be regarded as a strong, pragmatic and operational specification of Karl Popper's propensity interpretation of probabilities.

$\mathcal{M}$-adhesive categories provide an abstract framework for a large variety of specification frameworks for modelling distributed and concurrent systems. They extend the well-known frameworks of adhesive and weak adhesive HLR categories and integrate high-level constructs such as attribution as in the case of typed attributed graphs.

In the current paper, we investigate $\mathcal{M}$-adhesive transformation systems including negative application conditions (NACs) for transformation rules, which are often used in applications. For such systems, we propose an original equivalence on transformation sequences, called permutation equivalence, that is coarser than the classical switch equivalence. We also present a general construction of deterministic processes for $\mathcal{M}$-adhesive transformation systems based on subobject transformation systems. As a main result, we show that the process obtained from a transformation sequence identifies its equivalence class of permutation-equivalent transformation sequences. Moreover, we show how the analysis of this process can be reduced to the analysis of the reachability graph of a generated Place/Transition Petri net. This net encodes the dependencies between rule applications of the transformation sequence, including the inhibiting effects of the NACs.

The main promotor of this special issue, Mioara Mugur-Schächter, organised a final debate for the one day conference dedicated to the theme of this special issue of Mathematical Structures in Computer Science.

In this paper, we investigate the problem of robust stability for a class of delayed neural networks of neutral-type with linear fractional uncertainties. The activation functions are assumed to be unbounded, non-monotonic and non-differentiable, and the delay is assumed to be time-varying and belonging to a given interval, which means that the lower and upper bounds of the interval time-varying delay are available. By constructing a general form of the Lyapunov–Krasovskii functional, and using the linear matrix inequality (LMI) approach, we derive several delay-dependent stability criteria in terms of LMI. Finally, we give a number of examples to illustrate the effectiveness of the proposed method.

It is difficult to design a controller directly for non-square multi-variable systems with time delay. In the current paper, we propose a new design method for an Internal Model Control PID controller based on a modified effective open-loop transfer function (MEOTF) for non-square processes with time delay. The MEOTF method is used to decompose the complex non-square process into several equivalent independent single-input/single-output processes. Using the Taylor Particle Swarm Optimisation (Taylor-PSO) model reduction method, the MEOTF of the non-square process is approximated by a reduced order form. The reduced form of the MEOTF is then used to design the Internal Model Control PID controller, which is then used for the original non-square process. To improve the robust stability, a first-order filter is added in the feedback loop. Finally, we present simulation results showing the validity and reliability of this method. In particular, our method has a strong anti-interference characteristic and retains its good control performance in the presence of model perturbation and interference.

Statistical entropy was introduced by Shannon as a basic concept in information theory measuring the average missing information in a random source. Extended into an entropy rate, it gives bounds in coding and compression theorems. In this paper, I describe how statistical entropy and entropy rate relate to other notions of entropy that are relevant to probability theory (entropy of a discrete probability distribution measuring its unevenness), computer sciences (algorithmic complexity), the ergodic theory of dynamical systems (Kolmogorov–Sinai or metric entropy) and statistical physics (Boltzmann entropy). Their mathematical foundations and correlates (the entropy concentration, Sanov, Shannon–McMillan–Breiman, Lempel–Ziv and Pesin theorems) clarify their interpretation and offer a rigorous basis for maximum entropy principles. Although often ignored, these mathematical perspectives give a central position to entropy and relative entropy in statistical laws describing generic collective behaviours, and provide insights into the notions of randomness, typicality and disorder. The relevance of entropy beyond the realm of physics, in particular for living systems and ecosystems, is yet to be demonstrated.

In recent years, under the dual pressure of environmental requirements and a series of conventional energy shortages, including power cuts, coal shortages and rising oil prices, there have been unprecedented opportunities for clean energy, and especially for the development and utilisation of solar energy. Hence, solar products have become increasingly popular because of the energy saving and environmental protection they offer. China's solar energy industry should be in the self-development mechanism, which is market-oriented and should act as a mainstay for enterprises. Scientifically forecasting the potential of the solar energy industry and rationally evaluating its status as a result of a market economy-oriented development is an effective means of building a low-carbon and harmonious society. In the work reported in this paper, we:

• – established a comprehensive evaluation index system, covering natural resources, economic conditions, policy support, technology and the market environment;

• – constructed a GA-SA model based on analysing the principles of GA (genetic algorithms) and SA (simulated annealing); and

• – applied these tools to predicting the potential of the solar power industry.

This paper addresses the H∞ state feedback stabilisation problem for networked control systems (NCSs) in the presence of time delays and packet losses. By introducing the concept of an effective sensor packet, the NCS is transformed into a new discrete-time switched model, where the parameters have a clear physical meaning and can be easily determined. In this framework, we derive the stability conditions of the closed-loop system in the H∞ sense, and also provide the corresponding H∞ stabilising controller design method. Finally, we give simulation and experimental results to demonstrate the effectiveness of the proposed approaches.

We provide motivation for and then study the synthesis of Petri nets. Synthesis can avoid the state exploration problem by guaranteeing correctness for the Petri net. We propose conditions to be imposed on a synthesis shared pb-type subnet for systems specified in Petri nets that ensure the preservation of the liveness and boundedness structural properties. Specifically, we propose a group of sufficient conditions, or both sufficient and necessary conditions, for liveness preservation and boundedness preservation. Possible applications of this synthesis method are illustrated through an example in the form of a flexible manufacturing system. These results are useful for studying the static and dynamic properties of Petri nets for analysing the properties of large complex systems.

The process of river health evaluation is subject to uncertainty and complexity. To address this, we establish a river health evaluation system based on entropy and multi-objective space theory. We apply an analytic hierarchy process (AHP) to calculate the weight of the first grade indexes, and then apply the entropy to calculate the weight of the second indexes. In this way, the health measure can be considered in terms of objective data and a subjective classification. The results of the computation show that the whole system provides a good measure of the health. The results express the measurement of the health of the river on different levels and for different aspects, which indicates that the evaluation method is feasible.

We propose an adaptive genetic algorithm (AGA) for the multi-objective optimisation design of a fuzzy PID controller and apply it to the control of an active magnetic bearing (AMB) system. Unlike PID controllers with fixed gains, a fuzzy PID controller is expressed in terms of fuzzy rules whose consequences employ analytical PID expressions. The PID gains are adaptive and the fuzzy PID controller has more flexibility and capability than conventional ones. Moreover, it can be easily used to develop a precise and fast control algorithm in an optimal design. An adaptive genetic algorithm is proposed to design the fuzzy PID controller. The centres of the triangular membership functions and the PID gains for all fuzzy control rules are selected as parameters to be determined. We also present a dynamic model of an AMB system for axial motion. The simulation results of this AMB system show that a fuzzy PID controller designed using the proposed AGA has good performance.

The function of airport gate assignment is to assign appropriate gates for arrival and departure flights and to ensure the flights are on schedule. A key task of airport ground operations is assigning the airport gate with high efficiency and a reasonable arrangement. In this paper we establish an optimised model based on the characteristics of both the flights (the flight type, flight down time and the number of passengers) and the airport gates (the ease of access of the airport gate). We give a representation of the solution space and a direct graph model of the airport gate configuration based on dynamic scheduling parallel machines. We design a method for solving the airport gate configuration based on an immune genetic algorithm. The simulation results show the effectiveness of this model and algorithm.

In wireless broadband communication systems, the inherent non-linearity of power amplifiers creates spectral growth beyond the signal bandwidth, which interferes with adjacent channels. It also causes distortions within the signal bandwidth. In this paper, we study five digital predistortion algorithms for linearising two different non-linear memory power amplifier models. The simulation results show that the proposed digital predistorter using different algorithms can improve the in-band distortion and out of band spreading in different ways. In particular, the DLMS algorithm with fast convergence can significantly suppress spectral regrowth (by 60dB), effectively compensating for the non-linearity of the power amplifier.

We present a novel robust control scheme that deals with multi-body spacecraft attitude tracking problems. The control scheme consists of a radial basis function network (RBFN) and a robust controller. By using the finite time convergence property of the terminal sliding mode (TSM), we derive a new online learning algorithm for updating all the parameters of the RBFN that ensures the RBFN has fast approximation for the parameter uncertainties and external disturbances. We design a robust controller to compensate RBFN approximation errors and realise the anticipative stability and performance properties. We can also achieve closed-loop system stability using Lyapunov stability theory.

No detailed knowledge of the non-linear dynamics of the spacecraft is required at any point in the entire design process, and the proposed robust scheme is simple and effective and can be applied to more complex systems. Simulation results demonstrate the good tracking characteristics of the proposed control scheme in the presence of inertial uncertainties and external disturbances.

We present a concept of robust optimisation design for the spring actuator in a 10 kV/12.5 kA vacuum circuit breaker. We assume the breaking and closing velocity characteristics, which are derived form the technical data of the interrupter, as the specifications for the problem, and take the lengths of the connecting rods of the actuator and the stiffness coefficients of the breaking and closing springs as the optimisation variables. The variance between the specifications and the velocities calculated at each breaking and closing point and the maximal variation allowed by the design variables within acceptable tolerances make up the multiple objective function. The optimal parameters for the spring actuator are given by solving a non-linear programming problem with multiple targets and two-level optimisation.

We consider the problem of the robust stability of a class of uncertain T–S fuzzy neutral systems with time delay under time-varying parametric uncertainties using the Lyapunov–Krasovskii approach, where the parametric uncertainty is assumed to be norm bounded. By choosing a new Lyapunov–Krasovskii function, we are able to propose less conservative robust stability criteria in terms of linear matrix inequalities (LMIs) such that the uncertain T–S fuzzy neutral system under consideration remains asymptotically stable. The reduced conservatism of the proposed stability criterion compared with recently reported results is attributed to our using the Jensen inequality. The obtained results can also reduce the computational complexity.

Numerical simulation is the generally used method for studying stochastic resonance (SR), which is a kind of non-linear phenomenon that usually occurs in non-linear bistable systems. It has been found that the input signal needs to be over-sampled during the numerical simulation of SR. In this paper we provide an explanation of this phenomenon based on a stability analysis of the bistable system. We begin by studying the stability of a discrete model of a bistable system in numerical simulations. We then give a theoretical derivation of the stability conditions for the simulation model with different parameters, and carry out numerical experiments to show that the results coincide with the predictions of the theory. We explain why the input signal needs to be over-sampled in the simulation and provides guidelines for the choice of system parameters for the bistable system and the sampling time step in the numerical simulation of SR. Finally, we present the results of simulations showing an example of SR occurring in a bistable system and an example of weak periodic signal detection when it is processed by a bistable system.